A thermally insulated vessel contains some water at $0^{\circ} C$ . The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given Latent heat of vaporization of water at $0^{\circ} C = 21 \times 10^{5} J / k g$ and latent heat of freezing water $= 3.36 \times 10^{5} J / k g$ . The maximum percentage amount of water that will be solidified in this manner will be

86.2 %

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33.6 %

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21 %

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24.36 %

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Solution

The correct option is A $86.2 %$
Let $m_{1}$ be the amount of water that freezes and $m_{2}$ be the amount of water that vaporizes.

Therefore, heat is taken from frozen water= Heat given to water vapors.

$⟹ m_{1} (3.36 \times 10^{5}) = m_{2} (21 \times 10^{5})$

$⟹ m_{2} = 0.16 m_{1}$

Percentage of water solidified= $\frac{m_{1}}{m_{1} + m_{2}} \times 100$ %

$= 86.2$ %

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